Information may be transmitted from a transmitter to a receiver over a communication channel, such as a satellite link, a fiber optic cable, or a copper cable. The information may include, e.g., analog voice information from a telephone conversation or digital data that is transmitted between two computers. Analog information is often transformed into a digital format before it is transmitted over a channel.
The transmitted information may be encoded into a sequence of symbols selected from a set of pre-defined symbols, known as an alphabet. Each of the symbols is represented by an electronic pulse, which is transmitted over the communication channel to a remote location. The sequence of pulses forms a signal that is received by the receiver. The receiver retrieves the symbols from the signal and decodes them to recover the transmitted information.
Communication channels typically distort the pulses as they are transmitted through the channels. The channels may add noise to the pulses. Certain types of additive noise, known as white noise, are evenly distributed at all frequencies. Thermal noise from copper wires is typically a source of white noise. Other types of additive noise, known as colored noise, may be concentrated at certain frequencies. Signals induced on a wire by an adjacent wire, which is known as crosstalk, are a typical source of colored noise.
The channel may also distort the amplitude or phase of the transmitted signals. As a result of this distortion, the pulses representing the symbols may be corrupted with information from other pulses in the sequence. The corruption is referred to as inter-symbol interference (ISI). There are two kinds of ISI. A pulse representing a particular symbol may be corrupted with information from an earlier pulse in the sequence. This is known as post-cursor ISI. Alternatively, the pulse may be corrupted with information from a future pulse in the sequence. This is known as pre-cursor ISI.
The receiver typically has a signal detector to detect symbols received from the channel. The detector may, for example, be in the form of a simple threshold detector or a maximum likelihood sequence decoder. The detector is typically optimized to detect symbols that have only been distorted by additive white Gaussian noise (AWGN). Consequently, colored noise and/or inter-symbol interference may cause errors when the symbols are detected.